@@ -686,8 +686,11 @@ def _do_check_nptimedelta(self, pyfunc, arr):
         np.random.shuffle(arr)
         self.assertPreciseEqual(cfunc(arr), pyfunc(arr))
         # Test with a NaT
-        arr[arr.size // 2] = 'NaT'
-        self.assertPreciseEqual(cfunc(arr), pyfunc(arr))
+        if numpy_version != (1, 21) and 'median' not in pyfunc.__name__:
+            # There's problems with NaT handling in "median" on at least NumPy
+            # 1.21.{3, 4}. See https://github.com/numpy/numpy/issues/20376
+            arr[arr.size // 2] = 'NaT'
+            self.assertPreciseEqual(cfunc(arr), pyfunc(arr))
         if 'median' not in pyfunc.__name__:
             # Test with (val, NaT)^N (and with the random NaT from above)
             # use a loop, there's some weird thing/bug with arr[1::2] = 'NaT'